Can you help me?

I'm trying to find a TV film I watched when I was younger, but I can't remember the name. I do, however remember that:

- Rudolph was in it, but not as a main character.
- There was a large bird (the baddie) in it who lived for one eon and then died (I think).
- Father Time was a character.
- It was set on New Years eve, and was basically about people trying to find a baby that was needed for the new year.
-It was done with puppets.
- It was shown on British TV every year in the christmas peiod.

If anyone knows what this is, I will be so happy. There may even be props for the winner. :D